Practice 4 Solutions

3 0 eat e3t 3 2 1 2 1 21 21 1 3 y 0 1 1 2 2 1 0 y e3t

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Unformatted text preview: t 3 −1 2 + e2t 3 4 4 , 2 × 2 Exercise Set C (distinct roots), November [6] Solve the di erential equation y = Ay where −3 2 , −3 2 A= λ = −1, 0 3 −2 3 −2 eAt = e−t y(0) = −2 2 −3 3 + 1 2 y = e−t −1 −1 + 2 2 + 2 3 [7] Solve the di erential equation y = Ay where A= λ = −3, 0 eAt = e−3t 3 −2 −1 , −2 −1 21 21 + 1 3 y ( 0) = 1 −1 −2 2 1 0 y= e−3t 3 1 3 [8] Solve the di erential equation y = Ay where A= λ = 0, 1 eAt = −1 −2 , 1 2 2 2 −1 −1 + et y(0) = −1 −2 1 2 1 0 y= 2 −1 + et −1 1 1 −2 , 2 × 2 Exercise Set D (repeated roots), November 2 × 2 Exercise Set D (repeated roots) Linear Algebra, Dave Bayer, November , [1] Find An where A is the matrix A= λ = −2, −2 An = (−2)n 1 3 −3 −5 10 01 + n (−2)n−1 3 3 −3 −3 [2] Find An where A is the matrix A= λ = 0, 0 A n = 0n 1 1 −1 −1 10 01 + n 0n−1 1 1 −1 −1 [3] Find An where A is the matrix A= λ = 1, 1 An = 0 −1 1 2 10 01 +n −1 −1 1 1 [4] Find An where A is the matrix A= λ = 4, 4 An = 4n 2 −1 4 6 10 01 + n 4n−1 −2 −1 4 2 [5] Find An where A is the matrix A= λ = 1, 1 An = 6 5 −5 −4 10 01 [6] Find An where A is the matrix A= 61 −1 4 +n 5 5 −5 −5 , 2 × 2 Exercise Set D (repeated roots), November λ = 5, 5 A n = 5n 10 01 + n 5n−1 1 1 −1 −1 [7] Find An where A is the matrix A= λ = −1, −1 An = (−1)n 4 −5 5 −6 10 01 + n (−1)n−1 5 −5 5 −5 [8] Find An where A is the matrix A= λ = −3, −3 An = (−3)...
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